Question 6 - A-Level Maths

Solve the equation $x ^ { 4 } - 10 x ^ { 2 } + 25 = 0$.
Given that $y = \frac { 2 } { 5 } x ^ { 5 } - \frac { 20 } { 3 } x ^ { 3 } + 50 x + 3$, find $\frac { \mathrm { d } y } { \mathrm {~d} x }$.
Hence find the number of stationary points on the curve $y = \frac { 2 } { 5 } x ^ { 5 } - \frac { 20 } { 3 } x ^ { 3 } + 50 x + 3$.
Solve the simultaneous equations $$y = x ^ { 2 } - 5 x + 4 , \quad y = x - 1$$
State the number of points of intersection of the curve $y = x ^ { 2 } - 5 x + 4$ and the line $y = x - 1$.
Find the value of $c$ for which the line $y = x + c$ is a tangent to the curve $y = x ^ { 2 } - 5 x + 4$.